Acoustic flow measurement device including a plurality of chordal planes each having a plurality of axial velocity measurements using transducer pairs

ABSTRACT

A self-checking ultrasonic flow meter for measuring fluid flow in a conduit which includes a plurality of transducers engaged with the conduit. The flow meter includes a signal processor in electrical communication with the transducers which produces a measurement of flow rate and an associated estimate of uncertainty due to changes that have affected the accuracy of the measured flow rate. The transducers form multiple transducer pairs positioned to form acoustic transmission paths that are co-located in two or more chordal measurement planes. A plurality of axial velocity measurements are made in each chordal plane. A method for measuring fluid flow in a conduit with an ultrasonic flow meter.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a divisional of U.S. patent application Ser. No. 15/074,709filed Mar. 18, 2016, which is a continuation of U.S. patent applicationSer. No. 14/153,809 filed Jan. 13, 2014, both of which are incorporatedby reference herein.

FIELD OF THE INVENTION

The present invention is related to a self-checking flow meter based onthe principles of ultrasonic transit time measurement. The flow metertherefore outputs a measurement of flow rate and an associated estimateof uncertainty due to changes that may have affected the accuracy of themeasurement system. In particular, the invention enables verification ofthe axial velocity in each chordal measurement plane of the flow meter.This technique enables accurate self-verification to be carried out inthe presence of complex non-axial flows including asymmetric rotationalflows, and in case of a discrepancy allows identification of the chordalmeasurement plane or planes that have contributed to the discrepancy. Italso uniquely allows identification of common-mode errors due tocontamination based on the measurements in individual chordalmeasurement planes. (As used herein, references to the “presentinvention” or “invention” relate to exemplary embodiments and notnecessarily to every embodiment encompassed by the appended claims.)

BACKGROUND OF THE INVENTION

This section is intended to introduce the reader to various aspects ofthe art that may be related to various aspects of the present invention.The following discussion is intended to provide information tofacilitate a better understanding of the present invention. Accordingly,it should be understood that statements in the following discussion areto be read in this light, and not as admissions of prior art.

Transit time ultrasonic flow meters are capable of high accuracyperformance over a wide range of application conditions. This has led totheir adoption in applications such as custody transfer of hydrocarbons,and measurement of nuclear feedwater flows.

To achieve high accuracy it is common for transit time ultrasonic flowmeters to employ multiple pairs of transducers to infer velocity on anumber of discrete paths. The velocity measurements can then becombined, along with information on geometry, to produce a measure ofvolumetric flowrate.

Two features of ultrasonic meters are particularly attractive in manyapplications. Firstly, they can be designed to be non-intrusive, that isto present no blockage to the flow, and consequently produceinsignificant pressure loss. Secondly, their self-diagnosticcapabilities are attractive in applications where routine in-situcalibration is difficult for practical or cost reasons.

Currently the self-diagnostic capabilities of transit time ultrasonicmeters are based on evaluation of parameters such as amplifier gain,signal-to-noise ratios, and velocity profile descriptors such asflatness, asymmetry and swirl [Peterson, S, Lightbody, C, Trail, J andCoughlan, L (2008) On-line condition based monitoring of gas USM's,Proceedings of the North Sea Flow Measurement Vorkshop, Scotland,October 2008; Kneisley, G, Lansing, J, Dietz, T (2009) Ultrasonic metercondition based monitoring—a fully automated solution, Proceedings ofthe North Sea Flow Measurement Workshop, Norway, October 2009.].However, as these parameters are difficult to relate directly to theuncertainty of the flow measurement, the use of meter diagnostics aloneis not presently regarded as sufficient as a means of flow meterverification. For example, in the UK the Measurement Guidelines of theoffshore oil and gas measurement regulator, while recognizing thebenefits of current diagnostic techniques, note that they have thedisadvantage that “diagnostic facilities are presently qualitative,rather than quantitative” [Department of Trade and Industry, Licensingand Consents Unit, Guidance Notes for Petroleum Measurement Under thePetroleum (Production) Regulations, December 2003, Issue 7.]. In orderto overcome this limitation, sometimes two flow meters are installed inseries, i.e. with one a short distance downstream of the other. Thisallows the volumetric flowrates from the two flow meters to be comparedwith one another, with the result that the verification is quantitative,rather than qualitative. Taking this concept a step further, it has alsobeen known to calculate two independent flow rate measurements using twoindependent subsets of transducers installed in a single meter body.

One example of such a meter design is the combination of a 4-path meterand a single path meter [Kneisley, G, Lansing, J, Dietz, T (2009)Ultrasonic meter condition based monitoring—a fully automated solution,Proceedings of the North Sea Flow Measurement Workshop, Norway, October2009], as illustrated in FIG. 1. A disadvantage of this design is thatthe single path meter is much more sensitive to distortions of the flowvelocity field than the 4-path meter. This difference in sensitivitymeans that when a difference is detected, there exists the possibilitythat the single path meter can be affected by a distortion of the flowfield that has a negligible effect on the 4-path meter. In the casewhere the four path meter is used as the primary measurement, this couldresult in false alarms, i.e. the difference detected does not reflect areduction in accuracy of the 4-path meter. For example, in thereferenced paper it is shown that when a flow conditioner upstream ofthe meter has one hole become blocked, there is virtually no effect onthe 4-path meter, whereas the effect on the single-path meter can begreater than 0.85%. If, for example, an alarm threshold of 0.5% was setfor the difference between the 4-path and single path result, theoutcome would be an alarm annunciation where in fact the 4-path meter iscontinuing to read accurately.

Other examples of this concept include using two similar but separategroups of ultrasonic paths, such as shown in FIGS. 2a, 2b, 3a and 3b .FIGS. 2a and 2b show an arrangement of eight paths where one set of fourpaths are all set at a first angle relative to the pipe axis and thesecond set of four paths are all set at the negative value of thatangle, such that the paths form a symmetrical X about the pipe axis whenviewed from above. In this example the first set of four paths would be1, 2, 3 and 4 and the second set 5, 6, 7 and 8. In FIG. 3 an alternativearrangement is used whereby each independent set of four paths has pathsselected alternately relative to the pipe axis. In FIGS. 3a and 3b , thefirst set of four paths would be A1, B1, C1 and D1 and the second setA2, B2, C2 and D2. However, both of the arrangements shown suffer from acommon weakness in that each group of four paths will still be affecteddifferently by distortions of the flow velocity field, particularly whencomplex non-axial flow fields such as asymmetric rotational are present.What will happen in such a case is that one group of four paths willproduce a result that will overestimate the flow rate, whilst the othergroup will underestimate the flow rate. Whilst this has some use indiagnosing flow conditions, it complicates the process of meterverification, as it is difficult to distinguish between an error in themeasurement system itself and a difference that is created by the flowvelocity field.

This limitation can be reduced in magnitude by use of a mechanical flowconditioning element installed upstream of the flow meter is employed toreduce the transverse flow components, but this negates the benefits ofa non-intrusive meter design.

A further disadvantage of the concept using two similar groups ofultrasonic paths such as shown in FIGS. 2a, 2b, 3a and 3b is that evenwhen a flow conditioner is used, some problems may be difficult todetect or quantify. If, for example, a uniform buildup of contaminationinside the meter body was to occur, then the output from each set offour paths would be affected equally, and detection of the problem wouldhave to rely on qualitative diagnostics such as amplifier gain, velocityprofile shape or comparison of sound velocities, as there would be noindicated difference in flow rates.

BRIEF SUMMARY OF THE INVENTION

The present invention is a self-checking ultrasonic flow meter thatprovides an output of flow rate plus an associated estimate ofuncertainty due to changes that could have affected the accuracy of themeasurement system. One aim of the invention is to ensure that theestimate of uncertainty is not affected by asymmetric rotational flows,therefore eliminating the need for mechanical flow conditioning. This isachieved by arranging transducers such that redundant measurements ofaxial velocity can be made in each chordal measurement plane of the flowmeter, i.e. multiple axial measurements are made in each chordal planein such a way that they are substantially independent of the effects ofnon-axial or transverse flow. This dictates that there should be aminimum of six nodes in each chordal measurement plane, where each nodeis either a single transducer or a single reflection point. The compoundaxial velocity measurements in each measurement plane are then used inthe computation of the flow rate, and comparison of individual in-planeaxial velocity measurements used in the assessment of the uncertainty.Another aim of the invention is to be able to detect path angle and pathlength changes that would result from contamination build up inside themeter body, and to be able to do this for each chordal plane withoutreference to the data from another chordal plane. To that end, thevelocity measurements within each chordal plane are made using pairs oftransducers arranged such that one path has a path length divided by acosine of the angle relative to the conduit axis that is different fromanother path in that same plane. Combining these constraints the flowmeter would have transducers forming a minimum of three traverses ineach chordal plane, at least one path having a path length or path anglethat is different to the others in that plane.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING

In the accompanying drawings, the preferred embodiment of the inventionand preferred methods of practicing the invention are illustrated inwhich:

FIG. 1 shows a combination of a 4-path and a single-path meter in onebody of the prior art.

FIGS. 2a and 2b, and 3a and 3b show two different combinations of 4-pathmeters in one body of the prior art.

FIG. 4 is an illustration of a single chordal measurement plane of thepresent invention.

FIGS. 5a and 5b are illustrations of the transit time measurementprinciple with axial and transverse velocity components shown.

FIG. 6 shows three direct paths in a single chordal plane.

FIGS. 7a and 7b show an arrangement of transducers and reflectors in onechordal plane according to one embodiment of the invention.

FIGS. 8a and 8b show an arrangement of transducers forming direct pathsin one chordal plane according to one preferred embodiment of theinvention.

FIGS. 9a and 9b show an arrangement of transducers and reflectorsforming two direct paths and one reflected path in one chordal planeaccording to the invention.

FIGS. 10a-10f show various arrangements of transducers and reflectorswhere some are shared by two or more paths such that the total number ofnodes can be reduced to 5, 4 or 3. FIG. 10a shows three direct paths ina single chordal plane with one transducer that is shared by all threepaths. FIG. 10b shows two reflected paths with one transducer that isshared by both paths. FIG. 10c shows two reflected paths with areflector that is shared by both paths. FIG. 10d shows two direct pathsand one reflected path with one transducer that is shared by two pathsand with a combined transducer/reflector that is another shared node.FIG. 10e shows two direct paths and one reflected path with threetransducers that are each shared by two paths. FIG. 10f shows two directpaths and one reflected path with two transducers that are each sharedby two paths and a combined transducer/reflector that is a node that isshared by all three paths.

FIG. 11 shows a meter with four chordal planes.

DETAILED DESCRIPTION OF THE INVENTION

Referring now to the drawings wherein like reference numerals refer tosimilar or identical parts throughout the several views, and morespecifically to FIGS. 4, 5 a, 5 b, 6, 7 a and 7 b thereof, there isshown an ultrasonic flow meter 10 for measuring fluid flow in a conduit26. The flow meter 10 comprises multiple transducer pairs 12 positionedto form acoustic transmission paths 14 that are co-located in two ormore chordal measurement planes 16, each plane having length to widthratio of less than 2.5. In each chordal measurement plane the transducerpairs 12 located in the chordal measurement plane are positioned to formacoustic transmission paths 14 that traverse at least once from one side18 of the plane to another side 20 of the plane. If all paths 14 aredirect from one transducer 22 to another transducer 22 of a transducerpair, there is a minimum of three traverses in each chordal plane and ifany paths 14 employ a reflection point 28, there is a minimum of fourtraverses such that in either case a sum of the number of paths 14 andthe number of traverses in each chordal plane is greater than or equalto six. The flow meter 10 has a signal processor 30 to cause thetransducers 22 to produce the necessary signals and to receive thesignals produced by the transducers 22 and perform the necessary signalprocessing and computations. Such a signal processor 30 would be similarto those currently produced by Cameron International for the Caldon LEFMseries of flowmeters.

The ultrasonic flow meter 10 may have three paths 14 per chordal planeand transmission is on a direct path between individual transducers 22,as shown in FIG. 6. The ultrasonic flow meter 10 may have two paths 14per chordal plane, each path being a reflected path with two traversesof the chordal plane and one reflection in each of the two paths 14, asshown in FIGS. 7a and 7b . The ultrasonic flow meter 10 may have threepaths 14 per chordal plane and transmission on two paths 14 is directbetween transducers 22, and one path is a reflected path with twotraverses of the chordal plane and one reflection point, as shown inFIGS. 9a and 9 b.

The present invention pertains to an ultrasonic flow meter 10 formeasuring fluid flow in a conduit 26, as shown in FIGS. 6 and 11. Theflow meter 10 comprises multiple transducer pairs 12 positioned to formpaths 14 that are co-located in two or more chordal measurement planes16 of the conduit 26. In each chordal measurement plane transducers 22of the transducer pairs 12 are positioned to form acoustic paths 14 thattraverse at least once from one side 18 of the plane to another; atleast one path has a different path length or angle relative to theother paths 14 in that particular chordal plane, such that a path lengthdivided by a cosine of the angle relative to the conduit 26 axis isdifferent from another path in that same plane.

The present invention pertains to an ultrasonic flow meter 10 formeasuring fluid flow in a conduit 26, as shown in FIGS. 6 and 11. Theflow meter 10 comprises multiple transducer pairs 12 positioned to formpaths 14 that are co-located in two or more chordal measurement planes16 of the conduit 26, such that the paths 14 form a minimum of threetraverses in each chordal measurement plane.

The ultrasonic flow meter 10 may have three direct paths 14 per chordalplane whereby a first pair of paths 14 (A and B) are used in thecomputation of an axial velocity measurement in the plane, and a secondin-plane axial velocity measurement is made using one of the pathsbelonging to that first pair of paths and a third path such that thesecond pair of paths is defined as A plus C or B plus C.

The ultrasonic flow meter 10 may have three direct paths 14 per chordalplane whereby two in-plane axial velocity measurements are made in eachplane according to equations:

$v_{axialAB} = \frac{\left( {v_{B} - {v_{A}\frac{Z_{A}X_{B}}{X_{A}Z_{B}}}} \right)}{\left( {1 - \frac{Z_{A}X_{B}}{X_{A}Z_{B}}} \right)}$$v_{axialBC} = \frac{\left( {v_{C} - {v_{B}\frac{Z_{B}X_{C}}{X_{B}Z_{C}}}} \right)}{\left( {1 - \frac{Z_{B}X_{C}}{X_{B}Z_{C}}} \right)}$

Other presentations of these equations are possible; therefore it issolution of simultaneous equations to eliminate the transverse velocityin the solution that is important, not the specific form of the finalequation used.

The present invention pertains to an ultrasonic flow meter 10 formeasuring fluid flow in a conduit 26, as shown in FIGS. 6, 7 a, 7 b and11. The flow meter 10 comprises multiple transducer pairs 12 positionedto form acoustic transmission paths 14 that are co-located in two ormore chordal measurement planes 16. The length of a chordal plane 16containing the paths 14 being less than 2.5 times the width of the plane16. In each chordal measurement plane 16 the transducer pairs 12 locatedin the chordal measurement plane 16 are positioned to form acoustictransmission paths 14 that traverse at least once from one side of theplane 16 to another side of the plane 15. Each transducer 22 orreflection point 28 defines a path node. The number of nodes per chordalplane 16 is equal to or greater than six.

In the case where any node is shared between one or more paths, thetotal number of nodes can be reduced accordingly. This would apply if acommon reflection point 28 it used for more than one path 14, or if amulti-directional transducer 22 is used at the end of two or more paths14, as shown in FIGS. 10a and 10b . One example would be a chordal plane16 where three direct paths 14 are formed by using a shared transducer22 at one side of the plane 16 for one end of each of the three paths14, and separate transducers 22 at the other side of the plane 16 forthe other end of each of the three paths 14, as shown in FIG. 10a . Inthat case, the number of nodes would be reduced from 6 to 4 as thesecond and third paths 14 are sharing a node with the first path 14.Another example would be a chordal plane 16 where two reflected paths 14are formed by using a shared transducer 22 for one end of each of thetwo paths 14, separate reflectors 28 at the other side of the plane 16,and separate transducers 22 at the other end of each path 14, as shownin FIG. 10b . In that case the number of nodes would be reduced from 6to 5 as the second path 14 is sharing a node with the first path 14. Yetanother example would be a chordal plane 16 where two reflected paths 14are formed by using four separate transducers 22 for each end of the twopaths 14 on one side of the plane 16, and a shared reflector 28 at theother side of the plane 16, as shown in FIG. 10c . In that case thenumber of nodes would be also reduced from 6 to 5 as the second path 14is sharing a node with the first path 14.

In a case where there are three paths 14 in a chordal plane 16 andtransmission on two paths 14 is direct between transducers 22 and onepath 14 is a reflected path 14 with two traverses of the chordal plane16, the number of nodes may be reduced from 7 to 5 if the two directpaths 14 share a transducer node between them at one end and another ofthe direct path transducers also serves as the reflector for thereflected path, as shown in FIG. 10 d.

In another case where there are three paths 14 in a chordal plane 16 andtransmission on two paths 14 is direct between transducers 22 and onepath 14 is a reflected path 14, the number of nodes may be reduced from7 to 4 if the two direct paths 14 share a transducer node between themat one end and each share a transducer node at the other side of theplane with one or the other end of the reflected path 14.

In another case where there are three paths 14 in a chordal plane 16 andtransmission on two paths 14 is direct between transducers 22 and onepath 14 is a reflected path 14, the number of nodes may be reduced from7 to 3 if the two direct paths 14 each share a transducer node with thereflected path 14 and a third shared transducer node serves both pathsand also serves as the reflector 28 for the reflected path 14, as shownin FIG. 10 e.

The present invention pertains to a method for measuring fluid flow in aconduit 26 with an ultrasonic flow meter 10. The method comprises thesteps of forming with multiple transducer pairs 12 positioned withrespect to the conduit 26 acoustic transmission paths 14 that areco-located in two or more chordal measurement planes 16, each chordalplane having a length to width ratio of less than 2.5 In each chordalmeasurement plane the transducer pairs 12 located in the chordalmeasurement plane are positioned to form acoustic transmission paths 14that traverse at least once from one side 18 of the plane to anotherside 20 of the plane. If all paths 14 are direct from one transducer 22to another transducer 22 of a transducer pair a minimum of threetraverses is desired in each chordal plane and if any paths 14 employ apoint of reflection 28 a minimum of four traverses is desired such thatin either case a sum of the number of paths 14 and the number oftraverses in each chordal plane is greater than or equal to six. Thereis the step of determining the fluid flow in the conduit 26 from signalsreceived by the transducers 22 after they have traveled along the paths14.

The present invention pertains to a self-checking flow meter 10 fordetermining fluid flow in a conduit 26, as shown in FIGS. 6, 7 a, 7 band 11. The flow meter 10 comprises a plurality of transducers 22engaged with the conduit 26. The flow meter 10 comprises a signalprocessor 30 in electrical communication with the transducers 22 whichcauses the transducers 22 to transmit acoustic signals through theflowing fluid or receive flow signals from the transducers 22 based onthe transmitted acoustic signals the transducers 22 receive and producesa measurement of flow rate and an associated estimate of uncertainty dueto changes that have affected the accuracy of the measured flow ratebased on the acoustic signals.

The signal processor 30 may provide verification of axial velocity ineach chordal measurement plane of the flow meter 10 for accurateself-verification in the presence of complex non-axial flows includingasymmetric rotational flows, and in case of discrepancy providesidentification of which chordal measurement planes have contributed tothe discrepancy. The transducers 22 are arranged such that two or moremeasurements of axial velocity can be made in each chordal measurementplane of the flow meter 10 so the two or more in-plane axialmeasurements made in each chordal measurement plane are substantiallyindependent of the effects of non-axial or transverse flow. For this towork effectively, all paths must be closely spaced in order thatrotation and development of the flow in the axial direction does nothave a significant effect. In other words, if the paths are separated bytoo great a distance, the velocity profile and swirl pattern at separatepaths in the same chordal plane will be different and it cannot beassumed that the axial and transverse components of velocity are thesame at each path in the chordal plane. Therefore, the paths shouldpreferably overlap or the length of the chordal plane should be lessthan 2.5 times its width.

The signal processor 30 may detect path angle and path length changesthat would result from contamination build up inside the flow meter 10,and does this for each chordal measurement plane without reference todata from another chordal measurement plane. The transducers 22 may formmultiple transducer pairs 12 positioned to form acoustic transmissionpaths 14 that are co-located in two or more chordal measurement planes16, in each chordal measurement plane the transducer pairs 12 located inthe chordal measurement plane are positioned to form acoustictransmission paths 14 that traverse at least once from one side 18 ofthe plane to another side 20 of the plane, if all paths 14 are directfrom one transducer 22 to another transducer 22 of a transducer pair, aminimum of three traverses is desired in each chordal plane and if anypaths 14 employ a point of reflection 28, a minimum of four traverses isdesired such that in either case a sum of the number of paths 14 and thenumber of traverses in each chordal plane is greater than or equal tosix.

The measurement system of the invention comprises a section of conduit26 housing multiple ultrasonic transducers 22, each transducer 22 beingused in conjunction with at least one other transducer 22 in order tomeasurements of ultrasonic transit time along paths 14 inside theconduit. Transducers 22 are positioned such that all of the paths 14fall in a number of discrete chordal measurement planes 16. In thiscontext a chordal measurement plane is a plane that intersects twopoints on the boundary of the conduit, is parallel with the central axis24 of the conduit, and has a length to width ratio of less than 2.5 asshown in FIG. 4.

Either direct or reflected paths 14 can be used or a combination ofboth. In a direct path the ultrasonic signals travel between transducers22 without a change of direction via a reflection point. In a reflectedpath, the path is made up of two or more traverses of the interior ofthe conduit 26 by means of reflection. Reflected paths may requireinstallation of a reflector at the intersection with the conduit or mayuse the conduit 26 wall as a reflector. A direct path therefore includesonly one traverse across the chordal measurement plane, whereas areflected path includes multiple traverses. The current inventiondiffers from prior art in that the transit time measurements are used toobtain at least two values of axial velocity for each chordalmeasurement plane, derived in such a manner that each axial velocityvalue is substantially immune to any velocity component transverse tothe plane. This imposes certain conditions on the configuration of paths14 in each chordal measurement plane. In terms of the number of paths 14and traverses desired in each chordal plane, the minimum requirement isfor two paths of two traverses each if only reflected paths 14 are used.Three or more paths and three or more traverses are desired if anydirect paths are used.

With reference to FIGS. 5a and 5b , it can be shown with certainassumptions that the transit time associated with a single traverse ofan ultrasonic path can be represented as follows:

$t_{up} = \frac{L}{c - {v_{axial}\cos\;\theta} - {v_{transverse}\sin\;\theta}}$$t_{down} = \frac{L}{c + {v_{axial}\cos\;\theta} + {v_{transverse}\sin\;\theta}}$Where L is the length of the traverse, c is the sound velocity,v_(axial) is the velocity component in the axial direction,v_(transverse) is the velocity component at 90 degrees to the axialdirection in the chordal measurement plane and θ is the effective pathangle. Introducing a calculated velocity term v for an individual pathwe can write:

$v = {\frac{L\left( {t_{up} - t_{down}} \right)}{2\cos\;\theta\; t_{up}t_{down}} = {{v_{axial} + {v_{transverse}\tan\;\theta}} = {v_{axial} + {\frac{X}{Z}v_{transverse}}}}}$

Now, using an example of three direct paths as shown in FIG. 6, it canbe written,

$v_{A} = {v_{axial} + {\frac{X_{A}}{Z_{A}}v_{transverse}}}$$v_{B} = {v_{axial} + {\frac{X_{B}}{Z_{B}}v_{transverse}}}$$v_{C} = {v_{axial} + {\frac{X_{C}}{Z_{C}}v_{transverse}}}$Where X and Z are the projected path lengths on the cross-sectional andaxial planes and the subscripts refer to paths A, B and C respectively.

With a system of two simultaneous equations and two unknowns, it ispossible to solve for the two unknowns. In this case, there are threeequations and therefore we can obtain v_(axial) and v_(transverse) forthat particular chordal plane from multiple combinations of the data.For example, if v_(axialAB) is denoted to represent the axial velocitycalculated using the measurements from paths A and B, and v_(axialBC) torepresent the axial velocity calculated using the measurements of pathsB and C, then the above equations can be solved as follows:

$v_{axialAB} = \frac{\left( {v_{B} - {v_{A}\frac{Z_{A}X_{B}}{X_{A}Z_{B}}}} \right)}{\left( {1 - \frac{Z_{A}X_{B}}{X_{A}Z_{B}}} \right)}$$v_{axialBC} = \frac{\left( {v_{C} - {v_{B}\frac{Z_{B}X_{C}}{X_{B}Z_{C}}}} \right)}{\left( {1 - \frac{Z_{B}X_{C}}{X_{B}Z_{C}}} \right)}$

This gives us two measures of axial velocity in that particular chordalmeasurement plane (which we call ‘in-plane axial’ velocities), both ofwhich are independent of the transverse velocity in the plane. Thismeans that any difference between the calculated values of in-planeaxial velocity will highlight errors in either the transit timemeasurement terms or the geometric terms of the equation, and will notbe affected by transverse flow. Note that in this particular example, athird axial in-plane velocity v_(axialAC) can also be calculated.

Similar outcomes can also be obtained for more complex assumptionsincluding adaptations to include practical issues such as recessedtransducers and the inclusion of time delay corrections. Furthermore, asimilar treatment can be carried out for reflected paths, wherecancelation of transverse flow can be effected within individual paths.

Calculation of the axial velocity in each plane now proceeds as follows:v _(plane) _(i) =f ₁(v _(axialAB) ,v _(axialBC) ,v _(axialAC),etc)

Where f₁ represents a function used to combine the measurements, i.e. anaxial velocity for a chordal measurement plane i is derived from all ofthe in-plane axial velocity measurements obtained for in that particularplane, and hence uses all of the measurements from the paths 14 that liein that plane. One preferred method of combining the in-plane axialvelocities is performing a simple average. However, more complex methodscould be used, such as applying weighting factors to each of thein-plane axial velocities or selecting just one of the path combinationsto use, without departing from the spirit of the invention.

Flowrate is then calculated by combining together the axial velocitymeasurement from each of the measurement planes 16 (which we will nowcall the ‘plane velocities’), along with any desired geometric and/orcalibration factors, e.g.Q=k _(h) k _(g) f ₂(v _(plane) ₁ , . . . ,v _(plane) _(n) )

Where k_(h) represents a hydraulic correction factor, k_(g) represents ageometric factor, and f₂ represents the scheme used to combine the axialvelocity measurements in order to obtain a representative mean. Thiscould involve, for example, schemes such as Gaussian quadrature, wherethe measurement planes 16 are positioned parallel to one another atlocations predetermined by the number of planes 16 and the planevelocities are then weighted accordingly. e.g.

$Q = {k_{h}k_{g}{\sum\limits_{i = 1}^{n}{w_{i}v_{{plane}_{i}}}}}$Alternatively, empirical or model based combination of the planevelocities could be used.

For determination of the uncertainty due to changes that could haveaffected the accuracy of the measurement system, the difference betweenin-plane axial velocities is calculated for each measurement plane.Using again the example of three direct paths 14 per plane it ispossible to calculate three difference values for the in-plane axialvelocities, e.g.Δ_(AB-AC) =v _(axialAB) −v _(axialAC)Δ_(AB-BC) =v _(axialAB) −v _(axialBC)Δ_(AC-BC) =v _(axialAC) −v _(axialBC)

The uncertainty in the plane velocity would hence be functionallyrelated to the difference values:u _(plane) _(i) =f ₃(Δ_(AB-AC),Δ_(AB-BC),Δ_(AC-BC))

Alternatively, instead of using difference values, alternativecomputational method could be applied, for example, the ratios of thein-plane axial velocities or a standard deviation could be used as theinput to the uncertainty estimation.

The estimation of uncertainty can easily be illustrated by example. Inthis simple example the axial velocity in the measurement plane iscalculated using three direct paths 14, at angles of 75, 60 and 45degrees. Note that this represents only one plane of the meter 10, theresults of which would later be combined with the other planes 16 todetermine the flow rate and overall uncertainty. The followingparameters are used in the calculation for this example:

Axial velocity in the measurement plane: 10 m/s

Transverse velocity in the measurement plane: 1 m/s

Speed of sound in the fluid: 1500 m/s

Width of measurement plane: 0.1 m

Table 1 below illustrates the measurement results in the case of asystem operating with no errors. The in-plane axial velocities arecalculated from three separate combinations of paths A, B and C. Asthere are no errors present, and the transverse velocity is eliminatedin the calculation of the in-plane velocities, the three results forcombinations AB, BC and AC are the same, and hence when we compare themagainst the other, the calculated deltas are zero, as is the error inthe plane velocity.

TABLE 1 Individual paths A B C Angle (degrees) 75 60 45 X (m) 0.1000.100 0.100 Z (m) 0.027 0.058 0.100 Error in tup (ns) 0 0 0 tup (ns)69182.33 77282.26 94772.34 tdown (ns) 68855.27 76680.16 93794.54In-plane axial velocities Plane velocity AB AC CB Average Error (m/s)(m/s) (m/s) (m/s) (%) 10.00 10.00 10.00 10.00 0.00% Absolute deltas ABvs AC AB vs BC AC vs BC Maximum 0.00% 0.00% 0.00% 0.00%

Now an error of 2 nanoseconds can be introduced into the upstreamtransit time measurement (tup) on path A. As shown in Table 2, now whenthe in-plane axial velocities, AB, AC and BC are computed, threedifferent results are obtained. It is also found that there is now anerror in the plane velocity result. Examining the deltas when we compareour in-plane axial velocity measurements, we find that for thisparticular case the maximum deviation (AB vs BC) has a magnitude that istwice the error in the average axial velocity. Hence, there is ameasured deviation that can be directly related to the uncertainty bymeans of a sensitivity coefficient.

TABLE 2 Individual paths A B C Angle (degrees) 75 60 45 X (m) 0.1000.100 0.100 Z (m) 0.027 0.058 0.100 Error in tup (ns) 2 0 0 tup (ns)69184.33 77282.26 94772.34 tdown (ns) 68855.27 76680.16 93794.54In-plane axial velocities Plane velocity AB AC CB Average Error (m/s)(m/s) (m/s) (m/s) (%) 9.93 9.97 10.00 9.97 −0.34% Absolute deltas AB vsAC AB vs BC AC vs BC Maximum 0.42% 0.72% 0.31% 0.72%

In general, the delta values will exceed the error in the planevelocity, as a result of the plane velocity being calculated frommultiple in-plane axial velocities. However, under some circumstances,if more than one error is present, it is possible that they can combinein a way that alters the sensitivity coefficient. To provide additionalinformation and some protection against such circumstances, in-planetransverse velocities can also be calculated, compared and used in theuncertainty estimation. Following on from the earlier parts of thedescription, transverse velocities can be calculated as follows:

$v_{transverseAB} = \frac{\left( {v_{B} - v_{A}} \right)Z_{A}Z_{B}}{\left( {{Z_{A}X_{B}} - {Z_{B}X_{A}}} \right)}$

The technique developed here can be implemented in many different waysby someone skilled in the art. The following descriptions cover justsome of the possible implementations:

In the implementation shown in FIGS. 7a and 7b , a chordal planecontains two paths 14, each of which has a single reflection and twotraverses. Different angles have been selected for each path so as toallow detection of common-mode errors according to the invention. Inthis configuration, each path delivers an in-plane axial velocitymeasurement directly. Therefore, the comparison of the two paths 14 todetermine the uncertainty in that measurement plane serves the purposeof the invention in this case. As each reflected path cancels thecontribution to the measurement of non-axial component of flow, onerelative disadvantage of this particular configuration is that nomeasurements of non-axial flow are available to compliment the analysisof the axial velocities.

In the implementation shown in FIGS. 8a and 8b , the chordal planecontains three direct single-traverse paths, with no reflections. Again,different path angles have been selected for these paths so as to allowdetection of common-mode errors. With this configuration, any pair ofpaths 14 can be combined to yield both an axial and a non-axial flowvelocity, which in an advantage when compared with the embodiment ofFIGS. 7a and 7b and hence the arrangement in FIGS. 8a and 8b ispreferred.

FIGS. 9a and 9b show a combination of reflected and direct paths in onechordal plane. In this case there are two direct paths and one reflectedpath. The two direct paths can be combined to give one measure of thein-plane axial velocity and the reflected path will yield another. Yetagain, the use of different path angles and path lengths will facilitatedetection of common-mode errors.

In each of the preceding examples, a minimum of two measures of in-planeaxial velocity are derived that are substantially independent of thetransverse flow velocity. In order for this to be achieved, a chordalplane should contain an arrangement of paths 14 where the sum of thenumber of traverses plus the number of paths 14 is equal to or greaterthan 6. For example, in FIGS. 7a and 7b , there are two paths each withtwo traverses so the so the sum of traverses plus paths equals six.Likewise in FIGS. 8a and 8b there are three paths each of which are asingle traverse, so the sum of traverses plus paths equals six. Morecomplex arrangements involving direct and reflected paths, or multiplereflections are also possible without departing from the spirit of theinvention. In FIGS. 9a and 9b , there are three paths, two of which havea single traverse and one of which has two traverses, so the sum oftraverses plus paths in that case is seven.

An alternative way of describing the same constraint is to consider eachtransducer 22 or reflection point 28 as a node in the chordal plane. Inthat case, FIGS. 7 and 8 show arrangements with six nodes each, and FIG.9 shows an arrangement of seven nodes, therefore the minimum number ofnodes per chordal plane is six. Arrangements with more than seven nodesare conceivable but add cost and complexity to little gain.

FIGS. 10a-10f show various arrangements of 22 and reflectors 28 wheresome are shared by two or more paths such that the total number of nodescan be reduced to 5, 4 or 3. FIG. 10a shows three direct paths 14 in asingle chordal plane 16 with one transducer 22 that is shared by allthree paths 14, reducing the number of nodes required from 6 to 4. FIG.10b shows two reflected paths 14 with one transducer 22 that is sharedby both paths 14, reducing the number of nodes required from 6 to 5.FIG. 10c shows two reflected paths 14 with a reflector 28 that is sharedby both paths 14, reducing the number of nodes required from 6 to 5.FIG. 10d shows two direct paths 14 and one reflected path 14 with onetransducer 22 that is shared by two paths 14 and with a combinedtransducer/reflector 32 that is another shared node, reducing the numberof nodes required from 7 to 5. FIG. 10e shows two direct paths 14 andone reflected path 14 with three transducers 22 that are each shared bytwo paths 14, reducing the number of nodes required from 7 to 3. FIG.10f shows two direct paths 14 and one reflected path 14 with twotransducers 14 that are each shared by two paths 14 and a combinedtransducer/reflector 32 that is a node that is shared by all three paths14, reducing the number of nodes required from 7 to 3.

A second example follows in which the in-plane axial velocities arecompared in order to detect a uniform buildup of contamination on theface all transducers 22 in a single chordal plane. In this example weare considering a chordal plane situated at a distance of 0.809 timesthe radius of a circular conduit of 16 inches in diameter. Similar tothe earlier numerical example, this example uses direct paths only. Thepath angles selected were 45, 65 and −55 degrees and the path lengthswere chosen such that the transducers 22 would be slightly recessedrelative to the internal diameter of the conduit. A velocity of soundvalue of 1380 m/s was assumed for the liquid, and 2200 m/s was assumedfor the contaminant, representing a thin layer of hydrocarbon wax.

By simulation, the sensitivity factor relating the difference betweenthe calculated in-plane velocities and the measurement error wasdetermined in advance as a function of the measured transverse flow.Table 3 below shows the results when the axial flow velocity is 5 m/s,the transverse flow is zero and there are no measurement errors orcontamination build-up. In this table it can be seen that all threein-plane axial velocity measurements agree and hence the estimateduncertainty is zero.

TABLE 3 Path velocities Path A 5.000 m/s Path B 5.000 m/s Path C 5.000m/s In-plane axial velocties AB 5.000 m/s BC 5.000 m/s AC 5.000 m/sMeasured 5.000 m/s (average) axial velocity Acual error 0.00% Transverseflow    0% Difference max 0.000 m/s from min Sensitivity factor 2.1011Estimated 0.00% uncertainty

Table 4 shows the results when the axial flow velocity is 5 m/s, thetransverse flow is zero and there is a wax buildup of 0.02 inches oneach transducer 22 face. It can be observed that the velocitymeasurement in that chordal plane would be in error by 0.2% and that thedifference between the in-plane velocity measurements can be used topredict an increased uncertainty of 0.19%.

TABLE 4 Path velocities Path A 5.010 m/s Path B 5.011 m/s Path C 5.013m/s In-plane axial velocties AB 5.010 m/s BC 5.012 m/s AC 5.007 m/sMeasured 5.010 m/s (average) axial velocity Acual error 0.20% Transverseflow    0% Difference max 0.005 m/s from min Sensitivity factor 2.1006Estimated 0.19% uncertainty

Table 5 shows the results when the axial flow velocity is 5 m/s, thetransverse flow is 1 m/s and there are no measurement errors orcontamination build-up. It can be observed that taken individually theindicated velocities on individual paths (A, B and C) differ owing tothe transverse flow, and that looking at these three measurements itwould be difficult to determine whether or not an error is present, butthat when the in-plane velocities are calculated from path combinationsAB, BC and AC, the three results agree, and the analysis results in anestimate of zero additional uncertainty.

TABLE 5 Path velocities Path A 6.000 m/s Path B 3.572 m/s Path C 7.145m/s In-plane axial velocties AB 5.000 m/s BC 5.000 m/s AC 5.000 m/sMeasured 5.000 m/s (average) axial velocity Acual error 0.00% Transverseflow   20% Difference max 0.000 m/s from min Sensitivity factor 1.5891Estimated 0.00% uncertainty

Table 6 shows the results when the axial flow velocity is 5 m/s, thetransverse flow is 1 m/s and there is a wax buildup of 0.02 inches oneach transducer 22 face. It can be observed that, taken individually,the indicated velocities on individual paths (A, B and C) differ owingto the combined effects of transverse flow and the wax build up and thatlooking at these three measurements it would be difficult to determinewhether or not an error is present. However, when the in-planevelocities are calculated from path combinations AB, BC and AC andcompared, the three results do not agree exactly, and the uncertaintyanalysis results in an estimate of 0.19% additional uncertainty. It canalso be observed, that the sensitivity factor, is different in tables 4and 6, as this parameter is adjusted as a function of the measuredtransverse flow to maintain the correct relationship between themeasured difference between the in-plane velocities and thecorresponding measurement uncertainty.

TABLE 6 Path velocities Path A 6.012 m/s Path B 3.580 m/s Path C 7.162m/s In-plane axial velocties AB 5.010 m/s BC 5.012 m/s AC 5.006 m/sMeasured 5.009 m/s (average) axial velocity Acual error 0.19% Transverseflow   20% Difference max 0.006 m/s from min Sensitivity factor 1.5885Estimated 0.19% uncertainty

In practice, the invention will most likely be implemented inhigh-accuracy meter designs that would employ the invention in multiplechordal planes 16, such as the arrangement of four chordal planes 16,with three paths in each shown in FIG. 11. While this illustration showsthe same embodiment of the invention being used in each plane (i.e.three direct paths), it is also possible that different combinationscould be used, such as the arrangement of FIG. 7 being used in one planeand the arrangement of FIG. 8 being used in another.

Nomenclature

Chordal plane 16: A plane that intersects two points on the boundary ofa conduit and extends in a direction that is parallel with the centralaxis 24 of the conduit.

Path 14: Intended route of ultrasound transmission through the fluidbetween two transducers.

Chordal path: Any path that is confined to a single chordal plane.

Direct path: A path where the intended route of transmission is directlybetween two transducers and does not involve a change of direction bymeans of reflection.

Reflected path: A path where the intended route of transmission connectstwo transducers via one or more reflection points. The reflection pointcould either be the conduit wall itself, or a reflector designed toredirect the path partway along the route of transmission.

Traverse: A straight segment of a chordal path between any two points,either two transducers, two reflectors, or one transducer and onereflector. A direct path has only one traverse, a path with onerefection has two traverses, and a path with two reflections has threetraverses.

Node: A transducer site or reflection point that defines one end of atraverse.

In-plane axial velocity: A measure of axial velocity that involves useof two or more traverses in a single chordal plane in order to obtain avelocity measurement that is substantially independent of any transverseflow component in that plane.

Axial velocity: The component of flow velocity in a direction parallelwith the central axis 24 of the conduit.

Transverse velocity: The component of flow velocity at 90 degrees to theaxial direction in the chordal measurement plane.

Although the invention has been described in detail in the foregoingembodiments for the purpose of illustration, it is to be understood thatsuch detail is solely for that purpose and that variations can be madetherein by those skilled in the art without departing from the spiritand scope of the invention except as it may be described by thefollowing claims.

The invention claimed is:
 1. A self-checking flow meter for determiningflow rate of fluid flow in a conduit comprising: a plurality oftransducers engaged with the conduit and located on a chordal plane; aplurality of reflection points located on the chordal plane; a pluralityof nodes, wherein each of the plurality of nodes is associated with oneof: the plurality of transducers; or the plurality of reflection points;and a signal processor in electrical communication with the plurality oftransducers, the signal processor configured to cause the plurality oftransducers to transmit acoustic signals via chordal paths through thefluid flow or receive flow signals via chordal paths from the pluralityof transducers based on the transmitted acoustic signals, wherein theplurality of transducers receive and produce: a measurement of flowrate; and an associated estimate of uncertainty due to changes that haveaffected accuracy of the measured flow rate based on the flow signals,wherein the measurement of the flow rate is determined via ultrasoniccommunication between the plurality of transducers and reflectorslocated in the chordal plane, and wherein at least one node of theplurality of nodes is part of two or more chordal paths.
 2. The flowmeter of claim 1 wherein the signal processor provides independentverification of axial velocity in each chordal measurement plane of theflow meter for accurate self-verification in presence of complexnon-axial flows including asymmetric rotation of flows, and in case ofdiscrepancy provides identification of the chordal measurement plane orplanes contributing to the discrepancy.
 3. The flow meter of claim 2wherein the plurality of transducers are arranged such that two or moremeasurements of axial velocity can be made in each measurement plane ofthe flow meter such that each of the two or more measurements of theaxial velocity made in each chordal measurement plane are substantiallyindependent of effects of non-axial or transverse flow.
 4. The flowmeter of claim 3 wherein the signal processor detects path angle andpath length changes that would result from contamination build up insidethe flow meter, and does this for each chordal measurement plane withoutreference to data from another chordal measurement plane.
 5. The flowmeter of claim 4 wherein the transducers form multiple transducer pairspositioned to form acoustic transmission paths that are co-located intwo or more chordal measurement planes, in each chordal measurementplane the transducer pairs located in the chordal measurement plane arepositioned to form acoustic transmission paths that traverse at leastonce from one side of the plane to another side of the plane, if allpaths are direct from one transducer to another transducer of atransducer pair, there is a minimum of three traverses in each chordalplane and if any paths employ a point of reflection, there is a minimumof four traverses such that in either case a sum of a number of pathsand a number of traverses in each chordal plane is greater than or equalto six.
 6. The flow meter of claim 1 having three paths per chordalmeasurement plane and transmission is on a direct path betweenindividual transducers.
 7. The flow meter of claim 1 having two pathsper chordal measurement plane, each path being a reflected path with twotraverses of the chordal measurement plane and one reflection in each ofthe two paths.
 8. The flow meter of claim 1 having three paths perchordal measurement plane and transmission on two paths is directbetween transducers, and one path is a reflected path with two traversesof the chordal measurement plane and one reflection point.
 9. The flowmeter of claim 1 wherein the plurality of nodes comprises each of theplurality of transducers or each of the plurality of reflection pointsor a combination of both, the plurality of nodes configured to define anend to a straight segment of a chordal path between any of the pluralityof transducers or the plurality of reflection points.
 10. The flow meterof claim 9 wherein: the plurality of nodes are unshared such that eachof the plurality of nodes provides and receives signals from anothersingle node of each of the plurality of nodes and the plurality of nodesconsists of 6 or 7 nodes.
 11. The flow meter of claim 9, wherein one ofthe plurality of nodes is shared by three paths.
 12. The flow meter ofclaim 9, wherein two of the plurality of nodes are each shared by twopaths.
 13. The flow meter of claim 9, wherein three of the plurality ofnodes are each shared by two paths.
 14. The flow meter of claim 9,wherein two of the plurality of nodes are each shared by two paths and athird node of the plurality of nodes is shared by three paths.
 15. Theflow meter of claim 1, wherein the paths in each chordal plane overlap.16. The flow meter of claim 1, wherein three direct paths are providedper chordal plane wherein two measurements of the axial velocity aremade in each plane according to equations:$v_{axialAB} = \frac{\left( {v_{B} - {v_{A}\frac{Z_{A}X_{B}}{X_{A}Z_{B}}}} \right)}{\left( {1 - \frac{Z_{A}X_{B}}{X_{A}Z_{B}}} \right)}$$v_{axialBC} = {\frac{\left( {v_{C} - {v_{B}\frac{Z_{B}X_{C}}{X_{B}Z_{C}}}} \right)}{\left( {1 - \frac{Z_{B}X_{C}}{X_{B}Z_{C}}} \right)}.}$17. The flow meter of claim 1, wherein the plurality of transducersreceive and provide the acoustic signals such that a total number ofchordal paths is less than a total number of the plurality oftransducers.
 18. A self-checking flow meter for determining flow rate offluid flow in a conduit comprising: a plurality of transducers engagedwith the conduit; a plurality of reflection points located on a chordalplane; a plurality of nodes, wherein each of the plurality of nodes isassociated with one of: the plurality of transducers; or the pluralityof reflection points; and a signal processor in electrical communicationwith the plurality of transducers configured to cause the transducers totransmit acoustic signals through the fluid flow or receive flow signalsfrom the transducers based on the transmitted acoustic signals, whereineach of the plurality of transducers are configured to: receive andproduce a measurement of flow rate; and provide independent verificationof axial velocity in each chordal measurement plane of the flow meterfor accurate self-verification in presence of complex non-axial flowsincluding asymmetric rotation of flows based on multiple chordal pathsbetween two or more transducers and one or more reflectors, and in caseof discrepancy provides identification of the chordal measurement planeor planes contributing to the discrepancy, wherein at least one node ofthe plurality of nodes is part of two or more chordal paths.
 19. Amethod for measuring fluid flow in a conduit with an ultrasonic flowmeter comprising steps of: forming with multiple transducer pairspositioned with respect to the conduit acoustic transmission pathschordal measurement planes, in each chordal measurement plane, whereinthe multiple transducer pairs located in the chordal measurement planeare positioned to form acoustic transmission paths that traverse atleast once from one side of the plane to another side of the plane; anddetermining the fluid flow in the conduit from flow signals received bytransducers from the paths and an associated estimate of uncertainty dueto changes that have affected accuracy of the measured flow rate basedon the flow signals, wherein the measurement of the flow rate isdetermined via ultrasonic communication between the multiple transducerpairs and one or more reflectors located in the chordal measurementplane, wherein at least one node of a plurality of nodes is part of twoor more of the acoustic transmission paths such that a total number ofacoustic transmission paths is less than a total number of transducersof the transducer pairs.